You have actually not specified what you will be doing at EI. You have specified what EI is into. When trying to get into a new firm this is how I would look at it.
1. Who are the people behind it?
Educational Initiatives People
The list is definitely impressive. Started by IIMA Alumni etc. Hence thumbs up on this.
2. What kind of job profile would I get.
Educational Initiatives Careers
There are plethora of career options mentioned here. So, whats important is whether I would do work which would help me learn a lot more than what I know now and whether the experience would be good. You should also understand whether you can get into a core team, new projects soon. Whether the team size is small enough to gain many responsibilities etc. More importantly, what kind of impact would I have at work.
3. The definite way to have a bad career is to join a company as a stop gap arrangement before CAT and do nothing much at work. I know people who have done this for 3 years and have nothing much to show in their resume. When people come around asking the stupid qn whether work experience is better for MBA, they forget to ask the more important qn, what type of work experience and what you learnt. If you have learnt nothing much in 3 years of work, the opportunity cost has been very high!
4. Understand Where do you stand in terms of CAT. Are you someone who is of the 99%ile+ level, 95%ile+ level or 75%ile level on an average day.
5. Just looking from a resume perspective, if you do managerial work soon at EI and targeting to join IIMs/Tope B Schools, EI is a better shot. If you are unsure about MBA, may join a average school, TCS would be a good shot. Am talking just in terms of resume. If all you do in EI is enter some data or create maths syllabi, the impact is lesser unless you do that at a very good scale. Hence it wont look attractive in your resume.
6. If you don't do an MBA, EI may not be a good option since career path is undefined. However, You can have the confidence to do well there. But risk free option would be TCS then.
If I were you, I would join EI. But I have my reasons straight. Think in a structured manner by asking yourself a lot of questions and doing What If's.